¿Cuáles son las reglas en la clase de Esteban?

Explain why the statement below is true or false.

Only a discreet person should be trusted with a secret.

Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases.
$r(t)=\sin t \mathbf{i}+\sin t \mathbf{j}+\sqrt{2} \cos t \mathbf{k}$

Find the sum of the infinite geometric series if it exists.

x/3 + x$^2$/9 + x$^3$/27 + ..., |x|<3

The hyperbolic sine function is defined as $\sinh x=\frac{e^x-e^{-x}}{2}$. (a). Determine its end behavior by evaluating $\lim _{x \rightarrow \infty} \sinh x$ and $\lim _{x \rightarrow-\infty} \sinh x$ (b). Evaluate $\sinh 0$ . Use symmetry and part (a) to sketch a plausible graph for $y=\sinh x$.

Write a rule for the $n$th term of the geometric sequence.

$$r=\frac{1}{3}, a_1=45$$

The effect of periodic surface heating (either daily or seasonal) on the interior of the earth may be modeled by

$$\begin{aligned} \frac{\partial u}{\partial t} & =k \frac{\partial^2 u}{\partial x^2}, \quad 0<x<\infty \\ u(x, 0) & =0 \\ u(0, t) & =A e^{i \sigma_0 t} \end{aligned}$$

where the real part of $u(x, t)$ is the temperature (and $x$ measures distance from the surface). Approximate $\bar{U}(\omega, t)$ for large $t$.

In later courses, it is shown that

$$(1+x)^n=1+n x+\frac{n(n-1)}{2 !} x^2+\frac{n(n-1)(n-2)}{3 !} x^3+\cdots$$

for any real number $n$ (not just positive integer values) and any real number $x$, where $|x|<1$. Use this series to approximate the given number to the nearest thousandth.

$$(1.01)^{1.5}$$

Compute the definite integral $\int _ { 0 } ^ { 4 } \cos \sqrt { x } d x$ and interpret the result in terms of areas.

The following data, stored in Core Appliances, list the number of shipments of core major household appliances in the United States from 2000 to 2017 (in millions).

$$\begin{array}{cc|cc} \text { Year } & \text { Shipments } & \text { Year } & \text { Shipments } \\ \hline 2000 & 38.4 & 2009 & 36.5 \\ 2001 & 38.2 & 2010 & 38.2 \\ 2002 & 40.8 & 2011 & 36.0 \\ 2003 & 42.5 & 2012 & 35.8 \\ 2004 & 46.1 & 2013 & 39.2 \\ 2005 & 47.0 & 2014 & 41.5 \\ 2006 & 46.7 & 2015 & 42.9 \\ 2007 & 44.1 & 2016 & 44.7 \\ 2008 & 39.8 & 2017 & 46.4 \end{array}$$

Fit a three-year moving average to the data and plot the results.

Draw diagonal segment BD in the figure for the previous problems. Note that we will use it as an auxiliary line for this problem. Is triangle BDF isosceles? Prove it or explain why not.

On June 18, James Whiley signed a $10,000.00 note payable with National Bank of Cressville. At his request, the bank drafted the note for a 3-month term, payable on September 18 , with 15% interest. Mr. Whiley proudly stated, "Since my company began in 1972, we have never had to borrow money for more than 90 days." The loan officer, believing that Mr. Whiley did not fully understand the terms of the note, explained that the company would be responsible for interest for the number of days between June 18 and September 18. That number, he continued, would be slightly more than 90 days.

Instruction

Determine the maturity value of the note on September 18. Use the actual number of days from June 18 in your calculation.

In the following exercise, determine whether the table gives the probability distribution of the random variable X. Explain your answer.

$$\begin{array}{lcccccc} \hline \boldsymbol{x} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline P(X=x) & 0.3 & 0.1 & 0.2 & 0.2 & 0.1 & 0.2 \\ \hline \end{array}$$

En tu opinión, ¿cuál estudiante contesta más preguntas en clase?